 Previous Article
 AMC Home
 This Issue

Next Article
An improved certificateless strong keyinsulated signature scheme in the standard model
Some new results on cross correlation of $p$ary $m$sequence and its decimated sequence
1.  School of Mathemetics & Computation Science, Anqing Normal University, Anqing, Anhui 246133, China 
2.  Department of Mathematic and Statistics, Centtal China Normal University, Wuhan, Hubei 430079, China 
3.  Department of Mathematic Sciences, Yangzhou University, Yangzhou, Jiangsu 225002, China, China 
References:
[1] 
A. W. Bluher, On $x^{q+1}+ax+b$,, Finite Fields Appl., 10 (2004), 285. doi: 10.1016/j.ffa.2003.08.004. Google Scholar 
[2] 
W. Chen, J. Luo and Y. Tang, Exponential sums from half quadratic forms and its applications,, in Proc. ISIT'14, (2014), 3145. Google Scholar 
[3] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a ternary msequence of period $3^{4k+2}1$ and its decimated sequence by $(3^{2k+1}+1)^{2}$ over 8,, in Proc. ISIT'10, (2010), 1268. Google Scholar 
[4] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a $p$ary msequence of period $p^{2m}1$ and its decimated sequence by $\frac{(p^m+1)^2}{2(p+1)}$,, IEEE Trans. Inf. Theory, 58 (2012), 1873. doi: 10.1109/TIT.2011.2177573. Google Scholar 
[5] 
H. Dobbertin, P. Felke and T. Helleseth, Niho type cross correlation functions via Dickson polynomials and Kloosterman sums,, IEEE Trans. Inf. Theory, 52 (2006), 613. doi: 10.1109/TIT.2005.862094. Google Scholar 
[6] 
T. Helleseth, Some results about the crosscorrelation function between two maximallinear sequence,, Discrete Math., 16 (1976), 209. Google Scholar 
[7] 
R. Lidl and H. Niederreiter, Finite Fields,, AddisonWesley, (1983). Google Scholar 
[8] 
J. Luo and K. Feng, On the weight distribution of two classes of cyclic codes,, IEEE Trans. Inf. Theory, 54 (2008), 5332. doi: 10.1109/TIT.2008.2006424. Google Scholar 
[9] 
J. Luo and K. Feng, Cyclic codes and sequences from generalized CoulterMatthews function,, IEEE Trans. Inf. Theory, 54 (2008), 5345. doi: 10.1109/TIT.2008.2006394. Google Scholar 
[10] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued cross correlation,, in Proc. IWSDA'11, (2011), 44. Google Scholar 
[11] 
J, Luo, Y. Tang and H. Wang, Exponential sums, cyclic codes and sequences: the odd characteristic Kasami case,, preprint, (). Google Scholar 
[12] 
G. J. Ness, T. Helleseth and A. Kholosha, On the correlation distribution of the CoulterMatthews decimation,, IEEE Trans. Inf. Theory, 52 (2006), 2241. doi: 10.1109/TIT.2006.872857. Google Scholar 
[13] 
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Crosscorrelation distribution of pary msequence of period $p^{4k}1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$,, IEEE Trans. Inf. Theory, 54 (2008), 3140. doi: 10.1109/TIT.2008.924694. Google Scholar 
[14] 
Y. Sun, Z. Wang, H. Li and T. Yan, The crosscorrelation distribution of a $p$ary msequence of period $p^{2k}1$ and its decimated sequence by $\frac{(p^k+1)^2}{2(p^e+1)}$,, Adv. Math. Commun., 7 (2013), 409. doi: 10.3934/amc.2013.7.409. Google Scholar 
[15] 
Y. Xia, C. Li, X. Zeng and T. Helleseth, Some results on crosscorrelation distribution between a $p$ary $m$sequence and its decimated sequences,, IEEE Trans. Inf. Theory, 60 (2014), 7368. doi: 10.1109/TIT.2014.2350775. Google Scholar 
show all references
References:
[1] 
A. W. Bluher, On $x^{q+1}+ax+b$,, Finite Fields Appl., 10 (2004), 285. doi: 10.1016/j.ffa.2003.08.004. Google Scholar 
[2] 
W. Chen, J. Luo and Y. Tang, Exponential sums from half quadratic forms and its applications,, in Proc. ISIT'14, (2014), 3145. Google Scholar 
[3] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a ternary msequence of period $3^{4k+2}1$ and its decimated sequence by $(3^{2k+1}+1)^{2}$ over 8,, in Proc. ISIT'10, (2010), 1268. Google Scholar 
[4] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a $p$ary msequence of period $p^{2m}1$ and its decimated sequence by $\frac{(p^m+1)^2}{2(p+1)}$,, IEEE Trans. Inf. Theory, 58 (2012), 1873. doi: 10.1109/TIT.2011.2177573. Google Scholar 
[5] 
H. Dobbertin, P. Felke and T. Helleseth, Niho type cross correlation functions via Dickson polynomials and Kloosterman sums,, IEEE Trans. Inf. Theory, 52 (2006), 613. doi: 10.1109/TIT.2005.862094. Google Scholar 
[6] 
T. Helleseth, Some results about the crosscorrelation function between two maximallinear sequence,, Discrete Math., 16 (1976), 209. Google Scholar 
[7] 
R. Lidl and H. Niederreiter, Finite Fields,, AddisonWesley, (1983). Google Scholar 
[8] 
J. Luo and K. Feng, On the weight distribution of two classes of cyclic codes,, IEEE Trans. Inf. Theory, 54 (2008), 5332. doi: 10.1109/TIT.2008.2006424. Google Scholar 
[9] 
J. Luo and K. Feng, Cyclic codes and sequences from generalized CoulterMatthews function,, IEEE Trans. Inf. Theory, 54 (2008), 5345. doi: 10.1109/TIT.2008.2006394. Google Scholar 
[10] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued cross correlation,, in Proc. IWSDA'11, (2011), 44. Google Scholar 
[11] 
J, Luo, Y. Tang and H. Wang, Exponential sums, cyclic codes and sequences: the odd characteristic Kasami case,, preprint, (). Google Scholar 
[12] 
G. J. Ness, T. Helleseth and A. Kholosha, On the correlation distribution of the CoulterMatthews decimation,, IEEE Trans. Inf. Theory, 52 (2006), 2241. doi: 10.1109/TIT.2006.872857. Google Scholar 
[13] 
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Crosscorrelation distribution of pary msequence of period $p^{4k}1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$,, IEEE Trans. Inf. Theory, 54 (2008), 3140. doi: 10.1109/TIT.2008.924694. Google Scholar 
[14] 
Y. Sun, Z. Wang, H. Li and T. Yan, The crosscorrelation distribution of a $p$ary msequence of period $p^{2k}1$ and its decimated sequence by $\frac{(p^k+1)^2}{2(p^e+1)}$,, Adv. Math. Commun., 7 (2013), 409. doi: 10.3934/amc.2013.7.409. Google Scholar 
[15] 
Y. Xia, C. Li, X. Zeng and T. Helleseth, Some results on crosscorrelation distribution between a $p$ary $m$sequence and its decimated sequences,, IEEE Trans. Inf. Theory, 60 (2014), 7368. doi: 10.1109/TIT.2014.2350775. Google Scholar 
[1] 
Yuhua Sun, Zilong Wang, Hui Li, Tongjiang Yan. The crosscorrelation distribution of a $p$ary $m$sequence of period $p^{2k}1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$. Advances in Mathematics of Communications, 2013, 7 (4) : 409424. doi: 10.3934/amc.2013.7.409 
[2] 
Xiaohui Liu, Jinhua Wang, Dianhua Wu. Two new classes of binary sequence pairs with threelevel crosscorrelation. Advances in Mathematics of Communications, 2015, 9 (1) : 117128. doi: 10.3934/amc.2015.9.117 
[3] 
Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zerosum linearquadratic differential game: Saddlepoint equilibrium sequence. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 120. doi: 10.3934/naco.2017001 
[4] 
Hua Liang, Jinquan Luo, Yuansheng Tang. On crosscorrelation of a binary $m$sequence of period $2^{2k}1$ and its decimated sequences by $(2^{lk}+1)/(2^l+1)$. Advances in Mathematics of Communications, 2017, 11 (4) : 693703. doi: 10.3934/amc.2017050 
[5] 
Long Yu, Hongwei Liu. A class of $p$ary cyclic codes and their weight enumerators. Advances in Mathematics of Communications, 2016, 10 (2) : 437457. doi: 10.3934/amc.2016017 
[6] 
Zilong Wang, Guang Gong. Correlation of binary sequence families derived from the multiplicative characters of finite fields. Advances in Mathematics of Communications, 2013, 7 (4) : 475484. doi: 10.3934/amc.2013.7.475 
[7] 
Aixian Zhang, Zhengchun Zhou, Keqin Feng. A lower bound on the average Hamming correlation of frequencyhopping sequence sets. Advances in Mathematics of Communications, 2015, 9 (1) : 5562. doi: 10.3934/amc.2015.9.55 
[8] 
Hua Liang, Wenbing Chen, Jinquan Luo, Yuansheng Tang. A new nonbinary sequence family with low correlation and large size. Advances in Mathematics of Communications, 2017, 11 (4) : 671691. doi: 10.3934/amc.2017049 
[9] 
Yanfeng Qi, Chunming Tang, Zhengchun Zhou, Cuiling Fan. Several infinite families of pary weakly regular bent functions. Advances in Mathematics of Communications, 2018, 12 (2) : 303315. doi: 10.3934/amc.2018019 
[10] 
Lanqiang Li, Shixin Zhu, Li Liu. The weight distribution of a class of pary cyclic codes and their applications. Advances in Mathematics of Communications, 2019, 13 (1) : 137156. doi: 10.3934/amc.2019008 
[11] 
Jacinto Marabel Romo. A closedform solution for outperformance options with stochastic correlation and stochastic volatility. Journal of Industrial & Management Optimization, 2015, 11 (4) : 11851209. doi: 10.3934/jimo.2015.11.1185 
[12] 
Zhenyu Zhang, Lijia Ge, Fanxin Zeng, Guixin Xuan. Zero correlation zone sequence set with intergroup orthogonal and intersubgroup complementary properties. Advances in Mathematics of Communications, 2015, 9 (1) : 921. doi: 10.3934/amc.2015.9.9 
[13] 
Limengnan Zhou, Daiyuan Peng, Hongyu Han, Hongbin Liang, Zheng Ma. Construction of optimal lowhitzone frequency hopping sequence sets under periodic partial Hamming correlation. Advances in Mathematics of Communications, 2018, 12 (1) : 6779. doi: 10.3934/amc.2018004 
[14] 
Yuk L. Yung, Cameron Taketa, Ross Cheung, RunLie Shia. Infinite sum of the product of exponential and logarithmic functions, its analytic continuation, and application. Discrete & Continuous Dynamical Systems  B, 2010, 13 (1) : 229248. doi: 10.3934/dcdsb.2010.13.229 
[15] 
Samuel T. Blake, Thomas E. Hall, Andrew Z. Tirkel. Arrays over roots of unity with perfect autocorrelation and good ZCZ crosscorrelation. Advances in Mathematics of Communications, 2013, 7 (3) : 231242. doi: 10.3934/amc.2013.7.231 
[16] 
Atsushi Yagi. Exponential attractors for competing species model with crossdiffusions. Discrete & Continuous Dynamical Systems  A, 2008, 22 (4) : 10911120. doi: 10.3934/dcds.2008.22.1091 
[17] 
Libin Mou, Jiongmin Yong. Twoperson zerosum linear quadratic stochastic differential games by a Hilbert space method. Journal of Industrial & Management Optimization, 2006, 2 (1) : 95117. doi: 10.3934/jimo.2006.2.95 
[18] 
Lucas C. F. Ferreira, Elder J. VillamizarRoa. On the existence of solutions for the NavierStokes system in a sum of weak$L^{p}$ spaces. Discrete & Continuous Dynamical Systems  A, 2010, 27 (1) : 171183. doi: 10.3934/dcds.2010.27.171 
[19] 
Adina Luminiţa Sasu, Bogdan Sasu. Exponential trichotomy and $(r, p)$admissibility for discrete dynamical systems. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31993220. doi: 10.3934/dcdsb.2017170 
[20] 
Lassi Roininen, Markku S. Lehtinen, Sari Lasanen, Mikko Orispää, Markku Markkanen. Correlation priors. Inverse Problems & Imaging, 2011, 5 (1) : 167184. doi: 10.3934/ipi.2011.5.167 
2018 Impact Factor: 0.879
Tools
Metrics
Other articles
by authors
[Back to Top]